Problem: Solve for $x$, $ -\dfrac{5}{8x + 16} = \dfrac{7}{10x + 20} + \dfrac{x + 6}{2x + 4} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $8x + 16$ $10x + 20$ and $2x + 4$ The common denominator is $40x + 80$ To get $40x + 80$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ -\dfrac{5}{8x + 16} \times \dfrac{5}{5} = -\dfrac{25}{40x + 80} $ To get $40x + 80$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ \dfrac{7}{10x + 20} \times \dfrac{4}{4} = \dfrac{28}{40x + 80} $ To get $40x + 80$ in the denominator of the third term, multiply it by $\frac{20}{20}$ $ \dfrac{x + 6}{2x + 4} \times \dfrac{20}{20} = \dfrac{20x + 120}{40x + 80} $ This give us: $ -\dfrac{25}{40x + 80} = \dfrac{28}{40x + 80} + \dfrac{20x + 120}{40x + 80} $ If we multiply both sides of the equation by $40x + 80$ , we get: $ -25 = 28 + 20x + 120$ $ -25 = 20x + 148$ $ -173 = 20x $ $ x = -\dfrac{173}{20}$